After moving backup software to SSR2013, I ran into the issue of exchange server running low on disk space;
Incoming emails stopped flowing; internal emails would still work.

4 Steps total

Step 1: OMG Email not working! - Diagnose the cause

With Emails, there are many places to look for issues;
check places like firewall/UTM, external email filters, exchange server etc

in my case i found that our external email filter was working; however sending a test email from the system would not hit my inbox;
the next point to check was our UTM, which also spools the emails and acts as a secondary filter;
checking the logs on the UTM i found that there were 400 emails spooled and error msg with "Insufficient system resources"

Step 2: Low Space = Exchange hits the "medium" pressure threshold

At a particular point in time, exchange will hit whats called the "medium" pressure threshold point.

At this point, internal emails will still flow, however (external) inbound internet email will not be received and any applications that use non-MAPI methods to send email will also stop flowing.

Step 3: Make space for Exchange

move some log files off the drive to make some space and let email flow continue

Step 4: check your backup settings - Perform Full VSS backup

VSS should be enabled on SSR for Exchange servers.

Quote from help file: -

"Lets you perform a full backup on the VSS storage and send a request for VSS to review its own transaction log. This option is used for Microsoft Exchange Server only.

Exchange VSS determines what transactions are already committed to the database and then truncates those transactions. Among other things, truncated transaction logs help keep the file size manageable and limits the amount of hard drive space that the file uses.

If you do not select this option, backups still occur on the VSS storage. However, VSS does not automatically truncate the transaction logs following a backup."​​

If you are using Symantec System Recovery 2013 or Backup Exec products; check the VSS settings and recommendations for exchange server.